1.
Consider the uniform distribution on [0,1]. Compute with proof.
lim P([1/4,1-e^(-n)])
n->infinity
2.
Suppose P([0,8/(4+n)]) = (2+e^(-n)) / 6 for all n = 1,2,3...
What must P({0}) be?
What is P([1/4,1-e^(-n)]) meant to mean? Are you saying that X is a continuous random variable that has a standard uniform pdf and P([1/4,1-e^(-n)]) means P(1/4 < X < 1 - e^(-n))? If so, where exactly is your difficulty?
Unless you explain the notation you're using I don't think too many people are going to be replying. (I'd thought post #2 made it obvious that clarification of your notation was needed - by me, at least).